What is the Greatest Common Factor of 33735 and 33748?

Greatest common factor (GCF) of 33735 and 33748 is 13.

GCF(33735,33748) = 13

We will now calculate the prime factors of 33735 and 33748, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33735 and 33748.

How to find the GCF of 33735 and 33748?

We will first find the prime factorization of 33735 and 33748. After we will calculate the factors of 33735 and 33748 and find the biggest common factor number .

Step-1: Prime Factorization of 33735

Prime factors of 33735 are 3, 5, 13, 173. Prime factorization of 33735 in exponential form is:

33735 = 3¹ × 5¹ × 13¹ × 173¹

Step-2: Prime Factorization of 33748

Prime factors of 33748 are 2, 11, 13, 59. Prime factorization of 33748 in exponential form is:

33748 = 2² × 11¹ × 13¹ × 59¹

Step-3: Factors of 33735

List of positive integer factors of 33735 that divides 33735 without a remainder.

1, 3, 5, 13, 15, 39, 65, 173, 195, 519, 865, 2249, 2595, 6747, 11245

Step-4: Factors of 33748

List of positive integer factors of 33748 that divides 33735 without a remainder.

1, 2, 4, 11, 13, 22, 26, 44, 52, 59, 118, 143, 236, 286, 572, 649, 767, 1298, 1534, 2596, 3068, 8437, 16874

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33735 and 33748. The biggest common factor number is the GCF number.
So the greatest common factor 33735 and 33748 is 13.

Also check out the Least Common Multiple of 33735 and 33748